Analysis and Logic

Front Cover
Cambridge University Press, 2002 - Mathematics - 267 pages
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This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
 

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Contents

Introduction
3
Normed Space Structures
10
Signatures
13
Ultrapowers of Normed Space Structures
17
Positive Bounded Formulas
21
Basic Model Theory I
31
QuantifierFree Formulas
34
Ultraproducts of Normed Space Structures
38
Actions of the Infinite Symmetric Group
133
Turbulence I Overview
137
Turbulence II Basic Facts
143
Turbulence III Induced Actions
146
Turbulence IV Some Examples
150
Turbulence V Calmness
152
Turbulence VI The First Main Theorem
157
Turbulence VII The Second Main Theorem
163

Basic Model Theory II
43
Isomorphic Ultrapowers
55
Alternative Formulations of the Theory
72
Homogeneous Structures
75
More Model Theory
79
Types
96
References
107
Index of Notation
111
Index
112
Actions of Polish Groups and Classification Problems
115
Introduction
117
The General GlimmEffros Dichotomy
120
Actions of Polish Groups
123
Actions of Countable Groups
126
Actions of Locally Compact Groups
131
References
183
Index
186
On Subspaces Asymptotic Structure and Distortion of Banach Spaces Connections with Logic
189
Introduction
191
Background material The 60s and 70s
194
The unconditional basic sequence problem and connections with distortion
208
Gowers dichotomy A block Ramsey Theorem
217
Distortion
223
Asymptotic structure
233
Ordinal Indices
244
The homogeneous Banach space problem
252
Concluding remarks
254
References
256
Index
265
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